Algebra

Solving equations

Definitions

Expression

= any form of showing a mathematical value

• ex. the number 2 may be "expressed" as either "2" or "1+1"
• more complex "expressions" involve variables, such as "2y -5 = 10"
  • here, the value (expression) "10" can also be "expressed" as "2y - 5"

Equation

= a statement that uses an equal sign (=)

• which means that the expressions on both side of the equal sign have the same value

Inverse Operation

= a method for isolating variables by adding or multiplying a value to both sides of an equation

• the "inverse operation" reduces the value of the property on the side of the variable to 1 or 0

• that way the variable becomes "isolated" on one side of the equation

• ex.:
  • x + 3 = 8
• the "inverse operation" adds -3 to both sides of the equation:
  • x + 3 - 3 = 8 - 3

• which leaves us with
  • x + 0 = 5
  • x = 5

Property

• = the rule that is applied to numbers in an equation
• the property applied must be the same for both sides of the equation!
• properties include
  • Addition property (or subtraction)
  • Multiplication property (or division)

Isolating the variable

• Equations are solved by "isolating the variable"
  • which means "expressing" the unknown value by itself on one side of an equation
    • ex. to solve, "4 + x = 6" , we want to "isolate" x, so that we have "x = ___"

Properties of Equality

• property = a rule
• equality = that both sides of the equation (equal sign) have the same value